Field-stiffening effect of magneto-rheological elastomers

Magneto-rheological elastomers (MREs) are a class of soft active materials known for their tunable stiffness. Dispersed with magnetic particles, these polymer-based composites tend to be stiffer under a magnetic field. Such a stiffening effect is often attributed to the magnetic interaction among filler particles, but the well-acknowledged dipole-interaction model fails to explain the stiffening effect in tension/compression, which was observed in experiments. Other mechanisms, such as the effect of non-affine deformation, have been proposed, but there is no conclusive evidence on the dominating mechanism for the field-stiffening effect. This paper investigates various filler-chain structures, and seeks to identify the ultimate origin of the field-stiffening effect in MREs. Two different methods are used for cross verification: a dipole-interaction model and a finite-element simulation based on continuum field theories. This paper studies both the shear and axial deformation of the material, with a magnetic field applied in the particle-chain direction. It is found that while the magnetic interaction between particles is indeed the major cause of the stiffening effect, the wavy chain structure is the key to the modulus increase. Besides, chain-chain interaction and non-affine deformation are shown to be insignificant. In addition, the dependence of the stiffening effect on filler concentration is calculated, and the results qualitatively agree with experimental observations. The models also predict some interesting results that could be easily verified by future experiments.

Thanks for your question. As we know, stable equilibrium is a state of a system which will be recovered spontaneously after a small perturbation. In the processing of an MRE, the magnetic particles are initially mixed in a liquid-like polymer, and then an external magnetic field is applied. The particles are magnetized and thus move in the matrix to make the field more aligned. In a non-uniform magnetic field, all the particles will move towards to the place with highest field gradient, and form into a pile. Even in a uniform magnetic field, without the viscosity of liquid polymer matrix, no stable equilibrium state exists. Let’s first assume the particles form into a straight chain structure, which aligns the field best. However, the particles are attracted to each other due to dipolar interaction, and will move towards each other. As the inter-particle distance reduces the inter-particle attraction becomes stronger. And the liquid polymer is unable to prevent the particles in a chain from contacting each other. If the particles are in perfectly spherical shape, they contact each other at a point, such a straight chain is unstable, a small perturbation will break the chain. In reality, the particles are seldom to be in spherical shape. And an equilibrium state is even harder to imagine. But it is possible that the particles form into a wavy chain such that the magnetic attraction can be balanced by the viscous force from liquid polymer.

Yi HanGraduate Student / Research AssistantDept. of Aerospace EngineeringIowa State University